The present invention relates to a matched filter and a receiver, more specifically, to a matched filter having a reduced number of complex multipliers and a receiver using the matched filter.
In the field of radio communication, various systems have been studied and put into practice, targeting for improvement of frequency use efficiency. One of them is orthogonal frequency division multiplexing (OFDM), which now is a leading mobile communications system for the fourth generation because of its effectiveness against the delay of multipath radio waves.
Kitamura et al., in “Low Power Consumption CMOS Digital Matched Filter: An application Example of the Plastic Hard Macro Technology” (Technical Report of Institute of Electronics, Information and Communication Engineers, Vo. 42, No. 4, 2001), discloses a matched filter. In particular, the report illustrates two types of code division multiple accesses (CDMAs), that is, data circulation type and code circulation type. The configuration of a data circulation type matched filter which adopts OFDM-based technologies is first explained with reference to FIG. 1. FIG. 1 is a block diagram of a data circulation type matched filter. In FIG. 1, a matched filter 400 is constituted of (N−1) stage serial delay circuits 401, N multiplication circuits 403, each receiving a symbol Y[k] (k=0, . . . , N−1) through a conjugation circuit 402, a summing circuit 404 for summing outputs of the multiplication circuits, and an absolute value circuit 405 for calculating an absolute value of the output from the summing circuit 404. A received signal SR is output, per clock, to each of the multiplication circuits 403 and multiplied by the symbol Y[k]. The operating principle of the matched filter is basically similar to that of a finite impulse response (FIR) digital filter, repeatedly calculating a correlation between input signal and filter coefficient.
Factor for the matched filter can be written as follows. Let L be an even number, and let C be the known data. Dividing the known data C by first half L/2 points and second half L/2 points to obtain,X=[0,C[L/2],C[L/2+1], . . . , C[L−1],0,0, . . . , 0,C[0],C[1], . . . , C[L/2−1]]  (Formula 1).To make the number of N be a power of 2, zeros are inserted into the head and in front of the first half L/2, as behind the second half L/2, to make an array X. Next, by using a series Y obtained by applying an inverse FFT to the array X, a correlation between the series Y and the received signal SR is calculated.
By nature of a correlation function, an output absolute value becomes the maximum when timing of the matched filter coefficient Y and timing of the received signal SR coincide with each other. At this time, the signal is cut out with a serial-parallel converter (SP converter) connected to the absolute value circuit 405. In this way, symbol timing can be detected. “0” at the head of the array X corresponds to direct current, and “0” in the middle corresponds to out-of-band frequency, each being excluded from the inverse FFT calculation. The direct current is excluded because a direct current portion changes by the circuit offset.
As for the matched filter coefficient Y, a signal whose autocorrelation sequence is close to impulse, subcarrier power of which is distributed roughly uniformly, and which has a low PAPR (Peak to Average Power Ratio), is suitable. As for a series with the above nature, there is the Chu series of the formula 2, which is a signal used for known data C. Let L be the length of a series (which is an arbitrary even number), and let M be an arbitrary integer. The CHU series is described in “Polyphase Codes with Good Periodic Correlation Properties”, by David C. Chu, IEEE Transactions on Information Theory, July 1972.C[k]=exp[j*π*M/N*k^2](k=0,1, . . . , L−1)  (Formula 2)
In the CHU series, the constant M and the series length L are relatively prime so as to increase the autocorrelation and decrease PAPR.
C[k] is plotted on graphs as shown in FIG. 2, when L=50, M=3, and N=64. In FIG. 2, the upper stage is a real part, and the lower stage is an imaginary part. To obtain an array X, C[k] is divided into the first half L/2 points and the second half L/2 points, and zeros are inserted, according to the formula 1, to make the size be N. The resulting array X is one “0” at the head, twenty-five of the second half L/2 points “C[L/2], C[L/2+1, . . . , C[L−1]”, and thirteen “0”s, and twenty-five of the first half L/2 points “C[1], . . . , C[L−2−1]”.
By applying an inverse FFT to the resulting array X, a series Y is plotted on graphs as shown in FIG. 3. In FIG. 3, the upper stage is a real part, and the lower stage is an imaginary part. An autocorrelation function and absolute value of the series Y are also plotted on graphs as shown in FIG. 4. In FIG. 4, the upper stage is autocorrelation, and the lower stage is magnitude. As one can see from FIG. 4, the series Y has a low PAPR and its autocorrelation has an impulse pattern. Here, the effective value of a known symbol Y is 0.1105, and the maximum magnitude is 0.2017. PAPR of the series Y is then found as:20 log 10(0.2017/0.1105)=5.228[dB].